Belt's 18th-inning home run gave the Giants a 2-1 win over the Washington Nationals in game two of the National League Division Series.
San Francisco now lead the best-of-five series 2-0, putting them in pole position to continue their post-season charge.
The Giants " champions in 2012 " have won 10 successive play-off matches.
They were made to work for six hours and 23 minutes to secure their latest win though, smashing a league record.
Asdrubal Cabrera's run in the third inning looked like it may be enough for the Nationals, who carried the lead into the ninth.
But down to their final out, the Giants dug deep, sending the game to extra innings when Pablo Sandoval's RBI double saw Joe Panik score.
Drama followed as Washington manager Matt Williams and second baseman Cabrera were ejected in the 10th inning.
With both sides forced to use several pitchers, squad depth proved crucial and Yusmeiro Petit lived up to his end of the bargain.
The Giants pitcher came on in the 12th and allowed just one hit in six scoreless innings.
And that allowed Belt to claim the plaudits as he smashed a home run on a fly ball to right field.
Hunter Strickland replaced Petit for the final inning and finished the job for the victorious Giants.
In Saturday's other match, the Los Angeles Dodgers drew level in their own National League Division Series against the St.Louis Cardinals.
The Dodgers won 3-2 to level the best-of-five series at one match apiece.
Los Angeles had A.J. Ellis and pitcher Zack Greinke score in the third but their two-run lead was cut in the eighth as the Cardinals hit back.
Matt Carpenter's home run saw himself and Oscar Taveras home, levelling the contest.
Matt Kemp sealed LA's win, though, with a homer of his own in the bottom of the eighth.